# CDS 140a Winter 2014 Homework 9

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 R. Murray Issued: 25 Feb 2014 (Tue) ACM 101b/AM 125b/CDS 140a, Winter 2014 Due: 5 Mar 2014 (Wed) @ noon

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1. Perko, Section 4.4, Problem 1a
2. Show that for $a + b \neq 0$ the system
<amsmath>
 \aligned
\dot x &= \mu x - y + a (x^2 + y^2) x - b (x^2 + y^2) y + O(|x|^4) \\
\dot y &= x + \mu y + a (x^2 + y^2) x + b (x^2 + y^2) y + O(|x|^4)
\endaligned

</amsmath>

has a Hopf bifurcaton at the origin at the bifurcation value $\mu = 0$. Determine whether it is supercritical or subcritical.